A Universal Integral

Based on a minimal set of axioms we introduce a general integral which can be defined on arbitrary measurable spaces. It acts on measures which are only (finite) monotone set functions and on measurable functions whose range is contained in the unit interval. We introduce the notion of integral equivalence of pairs of measures and functions which leads us to a special important general integrals called universal integral. Several special types of such functionals, including extremal ones, are characterized. Key words. General integral, monotone set function, integral equivalence, universal integral, Choquet integral, semicopula.

• Type: Conference
• Year: 2007
• Where: EUSFLAT
• Authors: Erich-Peter Klement, Radko Mesiar, Endre Pap
• Keywords: EUSFLAT 2007, General Integral, Integral Equivalence, Monotone Set Function